Re: Simplifying with assumptions

*To*: mathgroup at smc.vnet.net*Subject*: [mg48992] Re: [mg48949] Simplifying with assumptions*From*: DrBob <drbob at bigfoot.com>*Date*: Sat, 26 Jun 2004 01:55:36 -0400 (EDT)*References*: <200406250658.CAA12398@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Here's a step that may be SLIGHTLY useful: Reduce[y == Sqrt[48 - n^2 + 8*x] && n \[Element] Integers && x \[Element] Integers && y \[Element] Integers] (n | x | y) \[Element] Integers && y >= 0 && x >= (1/8)*(-48 + y^2) && (n == -Sqrt[48 + 8*x - y^2] || n == Sqrt[48 + 8*x - y^2]) or Solve[y == Sqrt[48 - n^2 + 8*x], x] Solve[y == Sqrt[48 - n^2 + 8*x], n] {{x -> (1/8)*(-48 + n^2 + y^2)}} {{n -> -Sqrt[48 + 8*x - y^2]}, {n -> Sqrt[48 + 8*x - y^2]}} Bobby On Fri, 25 Jun 2004 02:58:13 -0400 (EDT), Mietek Bak <mietek at icpnet.pl> wrote: > Hello, > > I'm a complete newcomer to Mathematica, so please excuse this possibly > silly question. > > I'm trying to determine if a formula will ever give an integer result, > assuming that all variables used in it are integer. I've been searching > through the built-in documentation, but my best guess didn't really do > anything: > > Simplify[Element[Sqrt[48 - n^2 + 8*x],Integers],Element[{n, x},Integers]] > > It would be best if I could somehow determine the set of combinations of > variables that would give an integer result -- if there are any. Is > there a way to do that in Mathematica? > > Thanks in advance, > Mietek Bak. > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Simplifying with assumptions***From:*"Mietek Bak" <mietek@icpnet.pl>